With that sort of qualification, seeing something like HBO’s Deadwood is absolutely classified as Western without much thought; while Let Him Go is very much removed from the typical timeframe one would expect.
Bringing in the reaction of Diane Lane to the table, Let Him Go becomes a bit murkier to place, especially when mentioning the factor of the time period.
In fact, the only thing you can really be certain of with a question about why Westerns are so prevalent through pop culture is the fact that it’s hard to nail things down to one, uniformed answer.
Most Westerns happen to take place in a bygone era closer to the Civil War, while Thomas Bezucha’s treatment of the material changes the setting from Larry Watson’s original 1951 setting to a 1962 time frame.